Trying to bevel a design
This is kind of similar I imagine to working with text objects in Blender so ill demo on that,

Your topology starts like this, Or something near this:


Go to Mesh>Clean Up>Limited Dissolve, which basically dissolves all edges based on the angle of faces they are connected to.

 

Thatll give you this:



You might go through and clean up your edges a little bit, just to even out a few really long triangles or what not. This step might be not necessary. Some times blender has to have an edge in one spot to figure out how to make a weird Ngon stay together. If that edge is weird try to connect other vertices Around it and then use Ctrl+X to dissolve the bad one. You should be left with this:  

Then you can add your Bevel Modifier, Use these settings:
, most importantly, Setting the Bevel method to Angle, otherwise it bevels every single edge, and set the Outer Miter to Arc to smooth out the sharp corners. Set the model to Smooth Shaded, check Harden Normals on the Bevel Modifier and you get this:

Let me know if you have any other questions!